Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8f5)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-21/4, b>=a

For fixed z and a=-21/4, b=-3/4

http://functions.wolfram.com/07.23.03.a8f5.01

Input Form

Hypergeometric2F1[-(21/4), -(3/4), 7/2, -z] == (4 Sqrt[2] (-204 - 3451 z - 52445 z^2 + 326734 z^3 - 120990 z^4 - 22791 z^5 - 5449 z^6 - 940 z^7 - 80 z^8 + (1/Sqrt[1 + z]) (204 + 3553 z + 54145 z^2 - 133286 z^3 - 174458 z^4 + 12021 z^5 + 2837 z^6 + 480 z^7 + 40 z^8)))/(1341153 z^(5/2) Sqrt[-1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]